1. Introduction to single-cell RNA-seq
2. Quality control and normalization
3. Survey of downstream analysis methodology

• Goal: identify a set of genes with high variability attributable to biology (over and above technical variability)
• Useful for vizualization, dimension reduction, clustering, marker gene selection, etc
• Challenging without orthogonal measurement of technical variability (e.g. spikeins)
  • with spikeins: select genes with variance significantly above mean-variance trend in control genes
  • without spikeins: select genes with variance significantly above overall mean-variance trend in all endogenous genes (assumes variance of most genes is purely technical)

• Useful to summarize & visualize relationships between cells in low dimensional space
• Commonly used approaches:
  • PCA (Principal Components Analysis)
  • tSNE (t-distributed Stochastic Neighbor Embedding)
  • UMAP (Uniform Manifold Approximation and Projection)
• Clustering can be carried out on reduced dimensions, but with caution

1. random initialization, then iterate 2 & 3
2. calculate two probabilities of similiarity (of being neighbors - perplexity parameter roughly governs how many neighbors to consider):
   • probability of similarity of points in high-dimensional space
   • probability of similarity of points in low-dimensional space
3. minimize difference between these probabilities using Kullback-Leibler (KL) divergence
   • KL divergence is a distance metric for distributions: \[ D_{KL}(P|Q) = \sum_i p(x_i) log(\frac{p(x_i)}{q(x_i)}) \]

• Becht et al 2018 (https://doi.org/10.1038/nbt.4314)
• UMAP attempts to map points to a global coordinate system that preserves local structure
• Similar conceptually as tSNE, but specifics are different (e.g. different distributional kernels)
• Comparable performance to tSNE, but slightly better at preserving distances and faster runtime

• Nonlinear methods (UMAP & tSNE)
  • density & distance of points not preserved
  • better at visualizing rare subtypes

image source: http://carbonandsilicon.net/rblogging/2018/02/27/UMAP_plots

• Hierarchical: build and cut dendrogram based on pairwise distance matrix
• K-means: iteratively assign cells to nearest cluster center
• Density-based: clusters are defined as areas of higher density (e.g. DBSCAN)
• Graph-based: assumes data can be represented as a graph structure; doesn’t require estimating pairwise distance matrix (e.g. SNN-Cliq)

• Goal: automatically identify subpopulations of cell types/states
• Many methods adapted/developed for single-cell to account for:
  • high dropout rate
  • batch effects
  • high dimensionality

Andrews & Hemburg 2018 (https://doi.org/10.1016/j.mam.2017.07.002)

• Many clustering algorithms require specification of the number of clusters (e.g. K in K-means)
• Different algorithms may provide vastly different clusterings

Risso et al 2018 (https://doi.org/10.1371/journal.pcbi.1006378)

• Single clustering:
  • Average silhouette: how similar a cell is to its own cluster (average distance within) compared to other clusters (average distance between); not efficient for large numbers of cells \[s(b) = \frac{\bar{d}_{\text{within}}(b) - \bar{d}_{\text{between}}(b)}{max(\bar{d}_{\text{within}}(b), \bar{d}_{\text{between}}(b))}\]
  • Modularity score: difference between number of within-cluster edges to the expected number under the null (random edges)
• Comparing two clusterings
  • Adjusted rand index: similarity measure between two clusterings based on number of cells grouped accordingly and adjusted for random groupings

• Duo et al. 2018: https://doi.org/10.12688/f1000research.15666.2
• Bioconductor package to explore results: DuoClustering2018

• Traditional differential expression for bulk RNA-seq aims at detecting shifts in mean (fold change)
• Read counts \(y_{bg}\) typically modeled with a two parameter distribution (e.g. mean \(\mu_{bg}\), dispersion \(\alpha_g\))
• Recall DESeq2 model given size factors \(s_b\): \[ y_{bg} \sim NB(\mu_{bg}, \alpha_g)\] \[\mu_{bg}=s_b q_{bg}\] \[ log_2(q_{bg}) = x_{b.}\beta_g \]

Korthauer et al 2016 (https://doi.org/10.1186/s13059-016-1077-y)

• scDD: Korthauer et al 2016 (https://doi.org/10.1186/s13059-016-1077-y)
• Key idea: subpopulations of cell type/state will manifest as multimodal expression distributions
• Approach: explicitly model within sample heterogeneity and identify genes with differential distributions (as opposed to differences in mean)

1. Test for global difference in distribution of expressed values with nonparametric two-sample Kolmogorov-Smirnov test: \[ D_{n,m} = sup_x |F_{1,n}(x) - F_{2,m}(x)|\] \[ \text{Reject at level } \alpha \text{ if } D_{n,m} > \sqrt{\frac{-(n+m)ln(\alpha)}{2mn}} \]
2. Test for difference in dropout: GLM adjusted for cellular detection rate
3. Classify significant genes into summary patterns:

• Fit \(K-\) component normal mixture models to normalized log transformed expression values within each condition
• Select \(K\) by BIC
• Select pattern based on number of components & their equality of means

Korthauer et al 2016 (https://doi.org/10.1186/s13059-016-1077-y)

• A common workflow will include detection of DE genes between discovered subtypes (clusters)
• Caution must be used in the interpretation of p-values here
• Since clusters are formed by maximizing differences in expression, it is not surprising to discover DE genes between clusters - we can even detect changes in null data
• We may only be interested in differences in average expression here

• MAST: Finak et al. 2015 (http://doi.org/10.1186/s13059-015-0844-5)
• Hurdle model that depends on whether gene \(g\) in cell \(b\) is expressed (Normalized log count \(Y_{bg} > 0\)) or not (\(Y_{bg} = 0\)): \[ logit(P(Y_{bg} = 0)) = X_b\beta^D_g\] \[ P(Y_{bg} | Y_{bg} > 0) \sim N(X_b\beta_g^C, \sigma_g^2) \]
• Obtain \(\chi_{n}^{2}\) and \(\chi_{m}^{2}\) likelihood ratio test statistics for \(\beta_g^D\) and \(\beta_g^C\), with \(n\) and \(m\) degrees of freedom, respectively
• Global test statistic for a change in either component is the sum of the two:
  • sum of \(\chi^2\) random variables yields another \(\chi^2\) with degrees of freedom equal to the sum of degrees of freedom of the two original variables: \[\chi_m^{2} + \chi_n^{2} \sim \chi_{n+m}^{2}\]

Soneson & Robinson 2018 (https://doi.org/10.1038/nmeth.4612)

• Some datasets may be so large that they do not fit into memory efficiently (or at all)
• Handy infrastructure for computing on data that is saved on disk - allows computation on subsets:
  • HDF5 - file format interfaced with read/write functionalities in Bioconductor packages (rhdf5, Rhdf5lib, beachmat)
  • DelayedArray, DelayedMatrixStats - Bioconductor packages that provide an ecosystem for storing and computing on disk-backed files just like you would ordinary matrices
• Configured for use in SingleCellExperiment and interfaces automatically with scater and scran
  • requires saving data as HDF5 format

library(TENxBrainData)
assay(TENxBrainData(), "counts", withDimnames = FALSE)

## <27998 x 1306127> HDF5Matrix object of type "integer":
##                [,1]       [,2]       [,3]       [,4] ... [,1306124]
##     [1,]          0          0          0          0   .          0
##     [2,]          0          0          0          0   .          0
##     [3,]          0          0          0          0   .          0
##     [4,]          0          0          0          0   .          0
##     [5,]          0          0          0          0   .          0
##      ...          .          .          .          .   .          .
## [27994,]          0          0          0          0   .          0
## [27995,]          1          0          0          2   .          0
## [27996,]          0          0          0          0   .          0
## [27997,]          0          0          0          0   .          0
## [27998,]          0          0          0          0   .          0
##          [,1306125] [,1306126] [,1306127]
##     [1,]          0          0          0
##     [2,]          0          0          0
##     [3,]          0          0          0
##     [4,]          0          0          0
##     [5,]          0          0          0
##      ...          .          .          .
## [27994,]          0          0          0
## [27995,]          1          0          0
## [27996,]          0          0          0
## [27997,]          0          0          0
## [27998,]          0          0          0

• For a gentle introduction to the nitty gritty details of how the DelayedArray framework works, see the tutorial “Effectively using the DelayedArray framework for users” from the 2019 Bioconductor meeting

• For practice using scater and scran with HDF5 files the tutorial “Analysis of Large Single-Cell RNA-Seq Datasets in R/Bioconductor”, also from the 2019 Bioconductor meeting

• scran: detection of highly variable genes, dimension reduction, clustering (Bioconductor)
• Seurat: detection of highly variable genes, dimension reduction, clustering, DE (CRAN)
• mbkmeans: minibatch K-means for large data (Bioconductor)
• scDD: differential distributions (Bioconductor)
• MAST: differential expression (Bioconductor)

Zappia, Phipson & Oshlack 2018 (https://doi.org/10.1371/journal.pcbi.1006245)

BiocManager::install("scDD")
BiocManager::install("MAST")